behavior of ind, = and equal, also fiddling with limit
Subject: behavior of ind, = and equal, also fiddling with limit
From: Stavros Macrakis
Date: Thu, 24 Sep 2009 12:56:10 -0400
On Thu, Sep 24, 2009 at 11:45 AM, Richard Fateman
<fateman at cs.berkeley.edu>wrote:
> is (ind=ind) returns true
> is (equal(ind,ind)) returns false.
>
I believe this is correct, though confusing. "=" is syntactic equality;
"equal" is semantic. Two ind's, like two NaN's, are syntactically/formally
identical, though they do not necessarily represent the same
number/interval. Actually, a more precise answer for equal(ind,ind) is
"unknown".
> limit(1/x,x,0) returns infinity but the document says it returns und.
>
Both seem correct to me.
> limit(sin(x),x,infinity) returns und
>
I believe this is correct. For non-real x, abs(sin(x)) -> inf for x->inf
and for real x, it is IND (limit set [-1,1]). So und is the only possible
answer.
> limit(sin(x),x,inf) returns ind
>
Inf represents positive real inf, so this is correct.
(ps. Mathematica says limit(sin(x),x,inf) is [-1,1], which was discussed
> earlier.]
>
Seems like a reasonable version of ind giving more info (the limit set).
-s